Přístupnostní navigace
E-application
Search Search Close
Publication detail
DIBLÍK, J. MEDINA, R.
Original Title
Exact asymptotics of positive solutions to Dickman equation
Type
journal article in Web of Science
Language
English
Original Abstract
The paper considers the Dickman equation. The number theory uses what is called a Dickman (or Dickman -de Bruijn) function, which is the solution to this equation defined by an initial function x(t)=1 if 0≤t≤1. The Dickman equation has two classes of asymptotically different positive solutions. The paper investigates their asymptotic behaviors in detail. A structure formula describing the asymptotic behavior of all solutions to the Dickman equation is given, an improvement of the well-known asymptotic behavior of the Dickman function, important in number theory, is derived and the problem of whether a given initial function defines dominant or subdominant solution is dealt with
Keywords
Dickman equation; positive solution; dominant solution; subdominant solution; large time behavior; asymptotic representation; delayed differential equation.
Authors
DIBLÍK, J.; MEDINA, R.
Released
15. 1. 2018
Publisher
Americal Institute of Mathematical Sciences
ISBN
1553-524X
Periodical
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Year of study
23
Number
1
State
United States of America
Pages from
101
Pages to
121
Pages count
21
URL
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695
BibTex
@article{BUT149494, author="Josef {Diblík} and Rigoberto {Medina}", title="Exact asymptotics of positive solutions to Dickman equation", journal="DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B", year="2018", volume="23", number="1", pages="101--121", doi="10.3934/dcdsb.2018007", issn="1553-524X", url="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14695" }